Introduction To Modulation And Demodulation

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Communications Contents– Introduction to Communication Systems– Analogue ModulationAM, DSBSC, VSB, SSB, FM, PM, Narrow band FM, PLL Demodulators, and FLL Loops– Sampling SystemsTime and Frequency Division multiplexing systems, Nyquist Principle, PAM, PPM, and PWM.– Principles of NoiseRandom variables, White Noise, Shot, Thermal and Flicker Noise, Noise in cascadeamplifiers– Pulse Code ModulationPCM and its derivatives, Quantising Noise, and Examples– Digital Communication TechniquesASK, FSK, PSK, QPSK, QAM, and M-ary QAM.– Case StudiesSpread Spectrum Systems, Mobile radio concepts, GSM and Multiple Access SchemesMobile radio

Introduction to Modulation andDemodulationThe purpose of a communication system is to transfer information from a source to a destination.In practice, problems arise in baseband transmissions,the major cases being: Noise in the system – external noiseand circuit noise reduces thesignal-to-noise (S/N) ratio at the receiver(Rx) input and hence reduces thequality of the output.Such a system is not able to fully utilise the available bandwidth,for example telephone quality speech has a bandwidth 3kHz, aco-axial cable has a bandwidth of 100's of Mhz. Radio systems operating at baseband frequencies are very difficult. Not easy to network.

MultiplexingMultiplexing is a modulation method which improves channel bandwidth utilisation.For example, a co-axial cable has a bandwidth of 100's of Mhz. Baseband speech is a o

1) Frequency Division Multiplexing FDMThis allows several 'messages' to be translated from baseband, where they are allin the same frequency band, to adjacent but non overlapping parts of the spectrum.An example of FDM is broadcast radio (long wave LW, medium wave MW, etc.)

2) Time Division Multiplexing TDMTDM is another form of multiplexing based on sampling which is a modulationtechnique. In TDM, samples of several analogue message symbols, each onesampled in turn, are transmitted in a sequence, i.e. the samples occupy adjacenttime slots.

Radio Transmission Aerial dimensions are of the same order as the wavelength, , of the signal(e.g. quarter wave /4, /2 dipoles). is related to frequency byλ cfwhere c is the velocity of an electromagnetic wave, and c 3x108 m/sec in free space.For baseband speech, with a signal at 3kHz, (3x103Hz)3x10 8λ 3x10 3 105 metres or 100km. Aerials of this size are impractical although some transmissions at Very Low Frequency (VLF) for specialistapplications are made. A modulation process described as 'up-conversion' (similar to FDM) allows the baseband signal to betranslated to higher 'radio' frequencies. Generally 'low' radio frequencies 'bounce' off the ionosphere and travel long distances around the earth,high radio frequencies penetrate the ionosphere and make space communications possible.The ability to 'up convert' baseband signals has implications on aerial dimensions and design, long distanceterrestrial communications, space communications and satellite communications. Background 'radio' noiseis also an important factor to be considered. In a similar content, optical (fibre optic) communications is made possible by a modulation process in whichan optical light source is modulated by an information source.

Networks A baseband system which is essentially point-to-pointcould be operated in a network. Some forms of accesscontrol (multiplexing) would be desirable otherwise theperformance would be limited. Analoguecommunications networks have been in existence for along time, for example speech radio networks forambulance, fire brigade, police authorities etc. For example, 'digital speech' communications, in whichthe analogue speech signal is converted to a digitalsignal via an analogue-to-digital converter give a formmore convenient for transmission and processing.

What is Modulation?In modulation, a message signal, which contains the information is used to control theparameters of a carrier signal, so as to impress the information onto the carrier.The MessagesThe message or modulating signal may be either:analogue – denoted by m(t)digital – denoted by d(t) – i.e. sequences of 1's and 0'sThe message signal could also be a multilevel signal, rather than binary; this is notconsidered further at this stage.The CarrierThe carrier could be a 'sine wave' or a 'pulse train'.Consider a 'sine wave' carrier:vc t Vc cos ωct φc If the message signal m(t) controls amplitude – gives AMPLITUDE MODULATION AM If the message signal m(t) controls frequency – gives FREQUENCY MODULATION FM If the message signal m(t) controls phase- gives PHASE MODULATION PM or M

Considering now a digital message d(t):If the message d(t) controls amplitude – gives AMPLITUDE SHIFT KEYING ASK.As a special case it also gives a form of Phase Shift Keying (PSK) called PHASE REVERSALKEYING PRK. If the message d(t) controls frequency – gives FREQUENCY SHIFT KEYING FSK. If the message d(t) controls phase – gives PHASE SHIFT KEYING PSK. In this discussion, d(t) is a binary or 2 level signal representing 1's and 0's The types of modulation produced, i.e. ASK, FSK and PSK are sometimes described as binaryor 2 level, e.g. Binary FSK, BFSK, BPSK, etc. or 2 level FSK, 2FSK, 2PSK etc. Thus there are 3 main types of Digital Modulation:ASK, FSK, PSK.

Multi-Level Message SignalsAs has been noted, the message signal need not be either analogue (continuous) orbinary, 2 level. A message signal could be multi-level or m levels where each levelwould represent a discrete pattern of 'information' bits. For example, m 4 levels

What is Demodulation?Demodulation is the reverse process (to modulation) to recover the message signalm(t) or d(t) at the receiver.

Summary of Modulation Techniques 1

Summary of Modulation Techniques 2

Modulation Types AM, FM, PAM

Modulation Types AM, FM, PAM 2

Modulation Types (Binary ASK, FSK,PSK)

Modulation Types (Binary ASK, FSK,PSK) 2

Modulation Types – 4 Level ASK, FSK,PSK

Modulation Types – 4 Level ASK, FSK,PSK 2

Analogue Modulation – AmplitudeModulationConsider a 'sine wave' carrier.vc(t) Vc cos( ct), peak amplitude Vc, carrier frequency c radians per second.Since c 2 fc, frequency fc Hz where fc 1/T.Amplitude Modulation AMIn AM, the modulating signal (the message signal) m(t) is 'impressed' on to theamplitude of the carrier.

Message Signal m(t)In general m(t) will be a band of signals, for example speech or video signals. Anotation or convention to show baseband signals for m(t) is shown below

Message Signal m(t)In general m(t) will be band limited. Consider for example, speech via a microphone.The envelope of the spectrum would be like:

Message Signal m(t)In order to make the analysis and indeed the testing of AM systems easier, it is common to makem(t) a test signal, i.e. a signal with a constant amplitude and frequency given bym tV m cosmt

Schematic Diagram for AmplitudeModulationVDC is a variable voltage, which can be set between 0 Volts and V Volts. Thisschematic diagram is very useful; from this all the important properties of AM andvarious forms of AM may be derived.

Equations for AMFrom the diagram vs t VDC m t cos ωc t where VDC is the DC voltage that canbe varied. The equation is in the form Amp cos ct and we may 'see' that the amplitudeis a function of m(t) and VDC. Expanding the equation we get:vs t VDC cos ωc t m t cos ωc t

Equations for AMNow let m(t) Vm cos mt, i.e. a 'test' signal,Using the trig identitywe havecosAcosB vs t VDC cos ωc t vs t VDC cos ωc t Vm cos ωmt cos ωc t 1 cos A B cos A B 2VmVcos ωc ωm t m cos ωc ωm t 22Components:Carrier upper sideband USBlower sideband LSBAmplitude:VDCVm/2Vm/2Frequency: c c m c – mfcfc fmfc fmThis equation represents Double Amplitude Modulation – DSBAM

Spectrum and WaveformsThe following diagramsrepresent the spectrumof the input signals,namely (VDC m(t)),with m(t) Vm cos mt,and the carrier cos ctand correspondingwaveforms.

Spectrum and WaveformsThe above are input signals. The diagram below shows the spectrum andcorresponding waveform of the output signal, given byvs tV DC cosctVm2coscmtVm2coscmt

Double Sideband AM, DSBAMThe component at the output at the carrier frequency fc is shown as a broken line withamplitude VDC to show that the amplitude depends on VDC. The structure of thewaveform will now be considered in a little more detail.WaveformsConsider again the diagramVDC is a variable DC offset added to the message; m(t) Vm cos mt

Double Sideband AM, DSBAMThis is multiplied by a carrier, cos ct. We effectively multiply (VDC m(t)) waveformby 1, -1, 1, -1, .The product gives the output signal vs tV DC m t cosct

Double Sideband AM, DSBAM

Modulation DepthConsider again the equationvs t VDC Vm cos ωmt cos ωc t , which may be written as Vvs t VDC 1 m cos ωm t cos ωc t VDC The ratio isVmVModulation Depth m mdefinedasthemodulationdepth,m,i.e.VDCVDCFrom an oscilloscope display the modulation depth for Double Sideband AM may bedetermined as follows:Vm2EmaxVDC2Emin

Modulation Depth 22Emax maximum peak-to-peak of waveform2Emin minimum peak-to-peak of waveform2 Emax 2 EminModulation Depth m 2 Emax 2 EminThis may be shown to equalVmas follows:VDC2 Emax 2 V DC V mm 2 Emin 2 V DC V m2VDC 2Vm 2VDC 2Vm4VmVm VDC2VDC 2Vm 2VDC 2Vm4VDC

Double Sideband Modulation 'Types'There are 3 main types of DSB Double Sideband Amplitude Modulation, DSBAM – with carrier Double Sideband Diminished (Pilot) Carrier, DSB Dim C Double Sideband Suppressed Carrier, DSBSC The type of modulation is determined by the modulation depth,which for a fixed m(t) depends on the DC offset, VDC. Note, when amodulator is set up, VDC is fixed at a particular value. In the followingillustrations we will have a fixed message, Vm cos mt and vary VDCto obtain different types of Double Sideband modulation.

Graphical Representation of ModulationDepth and Modulation Types.

Graphical Representation of ModulationDepth and Modulation Types 2.

Graphical Representation of ModulationDepth and Modulation Types 3Note then that VDC may be set to givethe modulation depth and modulationtype.DSBAM VDC Vm, m 1DSB Dim C 0 VDC Vm,m 1 (1 m )DSBSC VDC 0, m The spectrum for the 3 main types ofamplitude modulation are summarised

Bandwidth Requirement for DSBAMIn general, the message signal m(t) will not be a single 'sine' wave, but a band of frequenciesextending up to B Hz as shownRemember – the 'shape' is used for convenience to distinguish low frequencies from highfrequencies in the baseband signal.

Bandwidth Requirement for DSBAMAmplitude Modulation is a linear process, hence the principle of superpositionapplies. The output spectrum may be found by considering each component cosinewave in m(t) separately and summing at the output.Note: Frequency inversion of the LSBthe modulation process has effectively shifted or frequency translated the basebandm(t) message signal to USB and LSB signals centred on the carrier frequency fcthe USB is a frequency shifted replica of m(t)the LSB is a frequency inverted/shifted replica of m(t)both sidebands each contain the same message information, hence either the LSB orUSB could be removed (because they both contain the same information)the bandwidth of the DSB signal is 2B Hz, i.e. twice the highest frequency in thebaseband signal, m(t)The process of multiplying (or mixing) to give frequency translation (or up-conversion)forms the basis of radio transmitters and frequency division multiplexing which will bediscussed later.

Power Considerations in DSBAM V pk Remembering that Normalised Average Power (VRMS)2 2 2we may tabulate for AM components as follows:VVvs t VDC cos ωc t m cos ωc ωm t m cos ωc ωm t 22ComponentCarrierUSBAmplitude pkVDCVm2PowerPowerVDC2VDC222LSBVm22V Vm m8 2 2 2m VDC8222V Vm m8 2 2 2m VDC822Total Power PT Carrier Power Pc PUSB PLSB

Power Considerations in DSBAMFrom this we may write two equivalent equations for the total power PT, in a DSBAM signal2222VVVVVPT DC m m DC m28824The carrier powerPc VDC22i.e.22and2VDCm 2VDCm 2VDCPT 288m2m2PT Pc Pc Pc44or2 m2 PT Pc 1 2 Either of these forms may be useful. Since both USB and LSB contain the same information auseful ratio which shows the proportion of 'useful' power to total power ism2PcPUSB4 PT m2Pc 1 2 m2 4 2m 2

Power Considerations in DSBAMFor DSBAM (m 1), allowing for m(t) with a dynamic range, the average value of mmay be assumed to be m 0.3 0.3 0.0215m2 4 2m 2 4 2 0.3 22Hence,Hence, on average only about 2.15% of the total power transmitted may be regardedas 'useful' power. ( 95.7% of the total power is in the carrier!)m21 Even for a maximum modulation depth of m 1 for DSBAM the ratio4 2m 2 6i.e. only 1/6th of the total power is 'useful' power (with 2/3 of the total power in thecarrier).

ExampleSuppose you have a portable (for example you carry it in your ' back pack') DSBAM transmitterwhich needs to transmit an average power of 10 Watts in each sideband when modulation depthm 0.3. Assume that the transmitter is powered by a 12 Volt battery. The total power will bem2m2PT Pc Pc Pc44m24 10 40 444.44 Wattswhere Pc 10 Watts, i.e. Pc 224m 0.3 Hence, total power PT 444.44 10 10 464.44 Watts.Hence, battery current (assuming ideal transmitter) Power / Volts i.e. a large and heavy 12 Volt battery.464.44 amps!12Suppose we could remove one sideband and the carrier, power transmitted would be10 Watts, i.e. 0.833 amps from a 12 Volt battery, which is more reasonable for aportable radio transmitter.

Single Sideband Amplitude ModulationOne method to produce signal sideband (SSB) amplitude modulation is to produceDSBAM, and pass the DSBAM signal through a band pass filter, usually called asingle sideband filter, which passes one of the sidebands as illustrated in the diagrambelow.The type of SSB may be SSBAM (with a 'large' carrier component), SSBDimC orSSBSC depending on VDC at the input. A sequence of spectral diagrams are shownon the next page.

Single Sideband Amplitude Modulation

Single Sideband Amplitude ModulationNote that the bandwidth of the SSB signal B Hz is half of the DSB signal bandwidth.Note also that an ideal SSB filter response is shown. In practice the filter will not beideal as illustrated.As shown, with practical filters some part of the rejected sideband (the LSB in thiscase) will be present in the SSB signal. A method which eases the problem is toproduce SSBSC from DSBSC and then add the carrier to the SSB signal.

Single Sideband Amplitude Modulation

Single Sideband Amplitude Modulationwith m(t) Vm cos mt, we may write:vs t VDC cos ωc t VmVcos ωc ωm t m cos ωc ωm t 22The SSB filter removes the LSB (say) and the output isvs t VDC cos ωc t Again, note that the output may beSSBAM, VDC largeSSBDimC, VDC smallSSBSC, VDC 0Vmcos ωc ωm t 2For SSBSC, output signal Vvs t m cos ωc ωm t 2

Power in SSB m2 From previous discussion, the total power in the DSB signal is PT Pc 1 2 22mm PT Pc Pc Pcfor DSBAM.44Hence, if Pc and m are known, the carrier power and power in one sideband may bedetermined. Alternatively, since SSB signal vs t VDC cos ωc t Vmcos ωc ωm t 2then the power in SSB signal (Normalised Average Power) is2VVV V PSSB DC m DC m228 2 2 2222VDCV mPower in SSB signal 282

Demodulation of Amplitude ModulatedSignalsThere are 2 main methods of AM Demodulation: Envelope or non-coherent Detection/Demodulation. Synchronised or coherent Demodulation.

Envelope or Non-Coherent DetectionAn envelope detector for AM is shown below:This is obviously simple, low cost. But the AM input must be DSBAM with m 1, i.e.it does not demodulate DSBDimC, DSBSC or SSBxx.

Large Signal OperationFor large signal inputs, ( Volts) the diode is switched i.e. forward biased ON, reversebiased OFF, and acts as a half wave rectifier. The 'RC' combination acts as a 'smoothingcircuit' and the output is m(t) plus 'distortion'.If the modulation depth is 1, the distortion below occurs

Small Signal Operation – Square LawDetectorFor small AM signals ( millivolts) demodulation depends on the diode square lawcharacteristic.The diode characteristic is of the form i(t) av bv2 cv3 ., wherev VDC m t cos ωc t i.e. DSBAM signal.

Small Signal Operation – Square LawDetectori.e.a VDC m t cos ωc t b VDC m t cos ωc t .2 2 aVDC am t cos ωc t b VDC 2VDC m t m t cos ωc t .2 2 12 aVDC am t cos ωc t bVDC 2bVDC m t bm t cos 2ωc t 22 12bVDC2bVDC m t bm t 2VDC aV amtcosωt bcos 2ωc t . DCc222222'LPF' removes components.2bVDC bVDC m t i.e. the output contains m(t)Signal out aVDC 2

Synchronous or Coherent DemodulationA synchronous demodulator is shown belowThis is relatively more complex and more expensive. The Local Oscillator (LO) must besynchronised or coherent, i.e. at the same frequency and in phase with the carrier in theAM input signal. This additional requirement adds to the complexity and the cost.However, the AM input may be any form of AM, i.e. DSBAM, DSBDimC, DSBSC orSSBAM, SSBDimC, SSBSC. (Note – this is a 'universal' AM demodulator and theprocess is similar to correlation – the LPF is similar to an integrator).

Synchronous or Coherent DemodulationIf the AM input contains a small or large component at the carrier frequency, the LOmay be derived from the AM input as shown below.

Synchronous (Coherent) Local OscillatorIf we assume zero path delay between the modulator and demodulator, then the idealLO signal is cos( ct). Note – in general the will be a path delay, say , and the LOwould then be cos( c(t – ), i.e. the LO is synchronous with the carrier implicit in thereceived signal. Hence for an ideal system with zero path delayAnalysing this for a DSBAM input VDC m t cos ωc t

Synchronous (Coherent) Local OscillatorVX AM input x LO VDC m t cos 2 ωc t VDC m t cos ωc t cos ωc t VDC m t 1 1 cos 2ωc t Vx 22 VDC VDCm t m t cos 2ωc t cos 2ωc t 2222We will now examine the signal spectra from 'modulator to Vx'

Synchronous (Coherent) Local Oscillator(continuedon nextpage)

Synchronous (Coherent) Local OscillatorandNote – the AM input has been 'split into two' – 'half' has moved or shifted up tom t V m t 2 fc cos 2ωc t VDC cos 2ωc t and half shifted down to baseband, DC and22 2

Synchronous (Coherent) Local OscillatorThe LPF with a cut-off frequency fc will pass only the baseband signal i.e.Vout VDC m t 22In general the LO may have a frequency offset, , and/or a phase offset, , i.e.The AM input is essentially either: DSB SSB(DSBAM, DSBDimC, DSBSC)(SSBAM, SSBDimC, SSBSC)

1. Double Sideband (DSB) AM InputsThe equation for DSB is VDC m t cos ωct where VDC allows full carrier (DSBAM),diminished carrier or suppressed carrier to be set.Hence, Vx AM Input x LOSince cosAcosB Vx Vx VDC m t cos ωc t .cos ωc Δω t Δφ 1 cos A B cos A B 2 VDC m t cos ω2c ωc Δω t Δφ cos ωc Δω t Δφ ωc t m t VVx DC cos 2ωc Δω t Δφ cos Δωt Δφ 22 VDCVcos 2ωc Δω t Δφ DC cos Δωt Δφ 22m t m t cos 2ωc Δω t Δφ cos Δωt Δφ 22Vx

1. Double Sideband (DSB) AM InputsThe LPF with a cut-off frequency fc Hz will remove the components at 2 c (i.e.components above c) and henceVout VDCm t cos( t φ) cos ωt φ 22VDC m t 22Consider now if is equivalent to a few Hz offset from the ideal LO.

Multiplexing Multiplexing is a modulation method which improves channel bandwidth utilisation. For example, a co-axial cable has a bandwidth of 100's of Mhz. Baseband speech is a only a few kHz . 1) Frequency Division Multiplexing FDM This allows several 'messages' to be translated from baseband, where they are all

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